Moments and Levers

A moment is the turning effect of a force about a pivot (also called a fulcrum).

$\boxed{M = F \times d}$

Where:

• $M$ = moment (in newton-metres, Nm)
• $F$ = force (in newtons, N)
• $d$ = perpendicular distance from the pivot to the line of action of the force (in metres, m)

Key point: The distance must be perpendicular (at right angles) to the force.

To increase the turning effect, you can:

1. Increase the force — push harder
2. Increase the distance from the pivot — apply the force further from the pivot

Everyday examples:

• Using a long-handled wrench instead of a short one
• Pushing a door at the handle (far from hinge) rather than near the hinge
• Using a crowbar — the long bar increases the distance from the pivot

When an object is in equilibrium (balanced), the sum of the clockwise moments about any pivot equals the sum of the anticlockwise moments.

$\sum M_{\text{clockwise}} = \sum M_{\text{anticlockwise}}$

This means if a seesaw is balanced: $F_1 \times d_1 = F_2 \times d_2$

Where $F_1, d_1$ are on one side and $F_2, d_2$ are on the other side of the pivot.

Conditions for Equilibrium

For an object to be in complete equilibrium:

1. The resultant force must be zero (no translation)
2. The resultant moment must be zero (no rotation)

A lever is a simple machine that uses a pivot to multiply the effect of a force.

Types of Levers

Class 1: Pivot is between the effort and the load.

• Example: Seesaw, scissors, pliers, crowbar

Class 2: Load is between the pivot and the effort.

• Example: Wheelbarrow, nutcracker, bottle opener

Class 3: Effort is between the pivot and the load.

• Example: Tweezers, fishing rod, human forearm

How Levers Work

Levers allow you to exert a smaller force over a larger distance to move a larger load over a shorter distance.

$\text{Effort} \times \text{distance from pivot to effort} = \text{Load} \times \text{distance from pivot to load}$

If the effort is further from the pivot than the load, you need less effort than the load — this gives a mechanical advantage.

Gears are toothed wheels that interlock. When one gear turns, it makes the other gear turn too.

Key Facts

• Interlocking gears turn in opposite directions
• A large gear driving a small gear increases speed but decreases the turning force (moment)
• A small gear driving a large gear decreases speed but increases the turning force (moment)
• The moment is transmitted through the gears

Gear Ratio

$\text{Gear ratio} = \frac{\text{number of teeth on driven gear}}{\text{number of teeth on driving gear}}$

A gear ratio greater than 1 means the output moment is multiplied (but the output speed is reduced).

The centre of mass is the point where the weight of an object acts.

• Low centre of mass + wide base = stable (hard to tip over)
• High centre of mass + narrow base = unstable (easy to tip over)

An object will topple when the line of action of the weight falls outside the base.

Examples:

• Racing cars are low and wide for stability
• A tall narrow vase tips easily
• Double-decker buses have heavy engines at the bottom to lower the centre of mass

Finding Centre of Mass (Irregular Object)

1. Hang the object from a pin, allowing it to swing freely
2. Hang a plumb line from the same pin
3. Draw a line along the plumb line on the object
4. Repeat from a different point
5. The centre of mass is where the lines cross

• Moment = force × perpendicular distance: $M = F \times d$ (units: Nm)
• Principle of moments: clockwise moments = anticlockwise moments (at equilibrium)
• Levers use moments to multiply forces
• Gears transmit and multiply moments (at the cost of speed)
• Centre of mass determines stability: low + wide = stable